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Abstract

We show how active transport of ions can be interpreted as an entropy facilitated process. In this interpretation, the pore geometry through which substrates are transported can give rise to a driving force. This gives a direct link between the geometry and the changes in Gibbs energy required. Quantifying the size of this effect for several proteins we find that the entropic contribution from the pore geometry is significant and we discuss how the effect can be used to interpret variations in the affinity at the binding site.

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... As suggested in the literature, [3][4][5][6][7] confinement can influence significantly the transport properties of diffusing entities, which is also a central idea of the current research. Spatial constriction of the pore causes decrease in volume of configuration space available for molecules in solution filling the channel's interior (also for K + ions), and in consequence-a drop in entropy. ...
... This simplification of the 3D channel system to 1D stems from the great difference of time scales of the ion motion within pore's cross section (where rapid local equilibration occurs) and along the channel axis (down the electrochemical gradient). 6 On the base of changes in channel's cross section, an entropic potential ∆S(x) can be defined in the direction of K + motion (along the channel axis-x) (Fig. 3), according to the formula, 3 ...
Article
We analyze the entropic effects of inner pore geometry changes of Kv 1.2 channel during membrane depolarization and their implications for the rate of transmembrane transport of potassium ions. We base this on the idea that spatial confinements within the channel pore give rise to entropic barriers which can both effectively affect the stability of open macroconformation and influence channel’s ability to conduct the potassium ions through the membrane. First, we calculate the differences in entropy between voltage-activated and resting states of the channel. As a template, we take a set of structures of channel pore in an open state at different membrane potentials generated in our previous research. The obtained results indicate that tendency to occupy open states at membrane depolarization is entropy facilitated. Second, we describe the differences in rates of K⁺ transport through the channel pore at different voltages based on the results of appropriate random walk simulations in entropic and electric potentials. The simulated single channel currents (I) suggest that the geometry changes during membrane depolarization are an important factor contributing to the observed flow of potassium ions through the channel. Nevertheless, the charge distribution within the channel pore (especially at the extracellular entrance) seems most prominent for the observed I/Imax relation at a qualitative level at analyzed voltages.
... [1][2][3][4][5][6][7][8][9] Particle invasion of a porous medium and drug delivery to cancerous tissues are examples where knowing the optimal conditions for transport is crucial. [10][11][12][13][14][15][16] Transport in micro-channels is virtually one-dimensional. Their irregular shapes, which in many cases can change over time, result in restrictions on the space that particles can occupy, leading to entropy variations along the length of the channels and over time. ...
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It is shown that the action of an oscillating force on particles moving through a deformable-walled channel causes them to travel greater distances than in the case of a rigid channel. This increase in the transport efficiency is due to an intensification of the stochastic resonance effect observed in corrugated rigid channels, for which the response to the force is maximal for an optimal value of the thermal noise. The distances traveled by the particles are even larger when the oscillation of the micro-channel is synchronized with that of an applied transverse force and also when a constant external force is considered. The phenomenon found could be observed in the transport of particles through elastic porous media, in drug delivery to cancerous tissues, and in the passage of substrates through transporters in biological membranes. Our results indicate that an appropriate channel design and a suitable choice of applied forces lead to optimal scenarios for particle transport.
... [1][2][3][4][5][6][7][8][9] Particle invasion of a porous medium and drug delivery to cancerous tissues are examples where knowing the optimal conditions for transport is crucial. [10][11][12][13][14][15][16] Transport in micro-channels is virtually one-dimensional. Their irregular shapes, which in many cases can change over time, result in restrictions on the space that particles can occupy, leading to entropy variations along the length of the channels and over time. ...
Article
Full-text available
It is shown that the action of an oscillating force on particles moving through a deformable-walled channel causes them to travel greater distances than in the case of a rigid channel. This increase in the transport efficiency is due to an intensification of the stochastic resonance effect observed in corrugated rigid channels, for which the response to the force is maximal for an optimal value of the thermal noise. The distances traveled by the particles are even larger when the oscillation of the micro-channel is synchronized with that of an applied transverse force and also when a constant external force is considered. The phenomenon found could be observed in the transport of particles through elastic porous media, in drug delivery to cancerous tissues, and in the passage of substrates through transporters in biological membranes. Our results indicate that an appropriate channel design and a suitable choice of applied forces lead to optimal scenarios for particle transport.
... Kobayashi et al. (5) discuss the feature that the entropy profile of the energy conversion in the pump is not taken into account. When we want to describe the pump function, this may become essential (22). The thermodynamic driving force for the conversion of a scalar to a vectorial process must be sought in the derivative −dμ/dγ. ...
... with the number f of degrees of freedom and the distance z from the reaction center in the funnel. Therefore, the free-energy potential has an entropic contribution going as GðzÞ ' Àk B T ln VðzÞ and the force exerted on the motor is FðzÞ ¼ À@ z GðzÞ [86][87][88]. During the release, the motor is thus propelled according to γ t dz=dt ¼ FðzÞ, giving the displacement z ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffi 2fD t Δt p over the time interval Δt, where D t ¼ k B T=γ t is the diffusion coefficient corresponding to Stokes' friction coefficient γ t . ...
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Colloidal motors with micrometer dimensions and no moving parts can be propelled by self-diffusiophoresis. Coupling between molecular concentration gradients generated by asymmetric surface chemical reactions and the velocity slip between colloidal particle and the surrounding fluid solution is responsible for propulsion. The interfacial properties involved in this propulsion mechanism can be described by nonequilibrium thermodynamics and statistical mechanics, disclosing the fundamental role of microreversibility in the coupling between motion and reaction. Among other phenomena, the approach predicts that propulsion by fuel consumption has the reciprocal effect of fuel synthesis by mechanical action.
... Furthermore, entropy provides a measure of the amount of coded information contained in the canonical genetic code [6], as well as a thermodynamic characterization of supercooled liquids [7,8] and amorphous materials [9,10]. Entropic effects are also crucial for mixture separation during adsorption processes [11,12], for the design of protein geometries to facilitate the active transport of ions [13], and in protein-protein binding for signal transduction and molecular recognition [14,15]. ...
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... To answer this question we use the concept studied in detail in[4][5][6][7][8]that the spatial confinement causes an entropic barrier. On the base of changes in channel's cross section an entropic potential ΔS(x) can be defined in the direction of K+ motion (along the channel axis) (Fig. 2), according to the formula: ...
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We analyze entropic effects of inner pore geometry changes of Kv 1.2 channel during membrane depolarization and their implications for the rate of transmembrane channel transport of potassium ions.
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We study biased, diffusive transport of Brownian particles through narrow, spatially periodic structures in which the motion is constrained in lateral directions. The problem is analyzed under the perspective of the Fick-Jacobs equation, which accounts for the effect of the lateral confinement by introducing an entropic barrier in a one-dimensional diffusion. The validity of this approximation, based on the assumption of an instantaneous equilibration of the particle distribution in the cross section of the structure, is analyzed by comparing the different time scales that characterize the problem. A validity criterion is established in terms of the shape of the structure and of the applied force. It is analytically corroborated and verified by numerical simulations that the critical value of the force up to which this description holds true scales as the square of the periodicity of the structure. The criterion can be visualized by means of a diagram representing the regions where the Fick-Jacobs description becomes inaccurate in terms of the scaled force versus the periodicity of the structure.